Finding the best regression model for shock waves from explosives

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Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the best nonlinear regression model for shock waves from explosives.  Here's our problem statement: The table below lists different amounts (in metric tons) of explosives and the corresponding value of the Richter scale for the explosions.  Construct a scatterplot and identify the mathematical model the best fits the given data.

Part 1

OK, the first part asks us to construct a scatterplot.  We can use StatCrunch to do this, so I'm going to dump my data into StatCrunch.  I'll resize this window so we can see everything better.  OK, now my data is in StatCrunch.

I could just use the scatterplot graphing option inside StatCrunch.  But I know I'm gonna have to make a regression model, and the regression model output includes a scatterplot.  Since I have to make the model anyway, it's the road I'm going to take.  I want to make a regression model and have the scatterplot come out of that regression model results.  The question is “Which model type do I need to be making?”  Is it linear?  Is it exponential?  Is it quadratic?  Is it logarithmic?  Is it a power function?  What type of model should we be making?

Without knowing in advance what type of problem goes with which model, you'll actually end up making all the models until you hit on the right one, and so you're gonna have to compare each of the different model types.  That would be useful in a class that was designed to teach you to be a good model maker.

This is a class in elementary statistics, and so I don't believe that's entirely appropriate.  So what I offer to my students is a reference sheet that tells them which model type they need to make, what's the general form of the model, and how do they get the numbers out of StatCrunch to transform them appropriately so that they put the right numbers into the answer fields for their assignments.

You can download a copy of this reference sheet if you want.  Go to aspiremountainacademy.com, find the blog post for this particular homework problem video, and you'll find there a link where you can download your own copy of this reference sheet.  You may not be able to use this in a testing situation (unless of course you're in my class; I allow my students to use it during tests).  But it will give you guidance on how to formulate the best model so that you can get to the end much quicker.  I also go over in the lecture video for this section many more details about how to actually use that reference sheet, so I'd highly recommend you check that out.

For purposes of working this problem, we're just going to go through what we already know if we knew how to use the reference sheet, which I do.  The model we need to make here for this problem is a logarithmic model, so to do that, I'm going to go to Stat –> Regression –> Simple Linear, select my x- and y- variables, and then scroll down here to the area that says Transformation.  For the X, I want to transform the X for the natural log.  I don't want any transformation for the Y.  And I want to select this box here for Use original units in graphs.  You'll see in a moment why we need to check this box.

I hit Compute!, and here are my results window.  If I click on to the second page, here's my scatterplot.  The reason why we check that box is because, if we didn't check the box, the line of best fit that we see here in the scatterplot would simply be a straight line, and it wouldn't conform to the type of model that we're trying to make.  So by checking that box you get a line of best fit that conforms to the model type you're trying to make.  Looking at the scatterplot, it's easy to see which of these answer options is the correct one.  Good job!

Part 2

Now the second part asks us to make the actual model, which we can do here.  Go back to the first page of my results.  For the logarithmic model, I simply take the intercept and slope right off the parameter estimates table and stick them into the model.  The general form for a logarithmic model is this one right here, so I select that and then put in my numbers to three decimal places.  Fantastic!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or if we can improve.  And if your stats teacher is boring or just doesn't care to help you learn stats, go to aspiremountainacademy.com, where you can find out more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.